> with(plots):
> a:=array(1..2);b:=array(1..2);c:=array(1..4);
> a[1]:=fieldplot([x,y],x=-3..3,y=-3..3):c[1]:=a[1]:
> a[2]:=fieldplot([-x,y],x=-3..3,y=-3..3):c[2]:=a[2]:
> b[1]:=fieldplot([x,-y],x=-3..3,y=-3..3):c[3]:=b[1]:
> b[2]:=fieldplot([-x,-y],x=-3..3,y=-3..3):c[4]:=b[2]:
> display(a);#need to adjust the sizes
> display(b);
> display(c);#hmmm too small
> a[1]:=spacecurve([cos(t),sin(t),t/(2*Pi)],t=0..6*Pi,axes=normal,orientation=[180,55]):
> a[2]:=spacecurve([t*cos(t),t*sin(t),t/(2*Pi)],t=0..6*Pi,axes=normal,orientation=[0,55]):
> display(a);
> #line integral
> #r(t):=[cos(t),sin(t)], t=0..Pi
> #F=[0,y];
> with(linalg):int(sin(t)*cos(t),t=0..Pi);
> r:=[cos(t),sin(t)];a:=0;b:=Pi;F:=[0,y];dr:=diff(r,t);
> integrand:=dotprod(subs({x=r[1],y=r[2]},F),dr,'orthogonal');
> Int(integrand,t=a..b)=int(integrand,t=a..b);
> r:=[cos(t),sin(t)];a:=0;b:=Pi/2;F:=[0,y];dr:=diff(r,t);
> integrand:=dotprod(subs({x=r[1],y=r[2]},F),dr,'orthogonal');
> Int(integrand,t=a..b)=int(integrand,t=a..b);
> r:=[cos(t),sin(t)];a:=0;b:=Pi;F:=[x,y];dr:=diff(r,t);
> integrand:=dotprod(subs({x=r[1],y=r[2]},F),dr,'orthogonal');
> Int(integrand,t=a..b)=int(integrand,t=a..b);
> r:=[cos(t),sin(t)];a:=0;b:=2*Pi;F:=[-y,x];dr:=diff(r,t);
> integrand:=dotprod(subs({x=r[1],y=r[2]},F),dr,'orthogonal');
> Int(integrand,t=a..b)=int(integrand,t=a..b);
> r:=[cos(t),sin(t)];a:=0;b:=0;F:=[-y,x];dr:=diff(r,t);
> integrand:=dotprod(subs({x=r[1],y=r[2]},F),dr,'orthogonal');
> Int(integrand,t=a..b)=int(integrand,t=a..b);
> r:=[t,7];a:=-3;b:=3;F:=[0,y];dr:=diff(r,t);
> integrand:=dotprod(subs({x=r[1],y=r[2]},F),dr,'orthogonal');
> Int(integrand,t=a..b)=int(integrand,t=a..b);
>